



6, 6, 7, 3, 0, 7, 0, 5, 2, 1, 6, 5, 4, 3, 7, 1, 2, 7, 2, 3, 9, 6, 0, 1, 6, 3, 9, 1, 3, 8, 8, 4, 1, 9, 9, 2, 4, 3, 7, 1, 6, 6, 8, 3, 0, 0, 6, 9, 1, 8, 5, 7, 2, 6, 4, 5, 7, 9, 2, 5, 6, 5, 1, 6, 5, 9, 0, 5, 4, 1, 2, 9, 2, 0, 2, 2, 8, 0, 2, 1, 5
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OFFSET

1,1


COMMENTS

This sequence is exactly equal to (Pi*h)/Spin(5/2), where h = Planck's Constant = A003676 and Spin(n/2) = h/(4*Pi) * sqrt(n(n+2)) = A003676/(10*A019694)) * sqrt(A005563(n)).
Observation: Where G is the universal gravitational constant = A070058 (= 6.67384(80)*10^11 m^3*kg^1*s^2), GM is the standard gravitational parameter, and M'_pbh is one estimate of the mass of a primordial black hole with evaporation time equal to the age of the universe (~ 10^11 kg; see link by Andrew Hamilton below), then this sequence approximates G*M'_pbh*(4*Pi^2)/GM = G*M'_pbh*seconds^2/meter^3. Were this formula to be exact, then, based on the CODATA 2010 value for G, the mass of such a primordial black hole, rounded to 6 decimal places, would be equal to 0.999885*10^11 kg, a figure subject to change based on future empirical measurements of G. Coincidentally, 99.9885(70)% is the estimated relative abundance of the hydrogen1 isotope (aka "protium") here on planet Earth.
Alternatively, from the formula for a pendulum, T = 2*Pi*sqrt(L/g), where L = Length, T = period and g is acceleration due to gravity, it follows that this sequence is exactly equal to (g*T^2*(hbar/2))/(L*Spin(5/2)); hbar/2 = h/(4*Pi) = A003676/(10*A019694) ~ A003676*A081821*A003671*A005600.  Raphie Frank, Jan 04 2013


LINKS

Table of n, a(n) for n=1..81.
B. J. Carr, Primordial black holes: do they exist and are they useful?, Queen Mary University of London.
Andrew Hamilton, Hawking Radiation, University of Colorado at Boulder.
Wikipedia, Gravitational constant
Wikipedia, Isotopes of hydrogen
Wikipedia, Pendulum
Wikipedia, Planck constant
Wikipedia, Spin (physics)


EXAMPLE

6.673070521654371272396016391388419924371668300691857264579256516590541...


CROSSREFS

Cf. A212002, A010490.
Sequence in context: A241057 A247253 A244293 * A070058 A160057 A190145
Adjacent sequences: A196734 A196735 A196736 * A196738 A196739 A196740


KEYWORD

nonn,cons


AUTHOR

Raphie Frank, Dec 21 2012


STATUS

approved



